DD is 11, and lets herself in after school for 2-3 hours in the afternoons. She makes herself a snack (often using microwave or oven or kettle (on pot noodle type things) - but she's not confident enough and nor are we about letting her use the gas hob while we're out). She does her homework, and any other jobs we've agreed (empty the dishwasher, or set the table for dinner). And then she looses all track of time in front of the Xbox.
We've left her for just over an hour at night, if DH is away for me to go to my pilates class. She finishes watching her show, makes her hot chocolate in the microwave and heads to bed - but I am not entirely convinced that she doesn't extend her bedtime slightly, as she's often suspiciously awake when I get home! 
But she would not be happy herself with being alone all day. And neither would we. There are many afternoons when I get a call from her, to check what she can eat but as often as not, a reason for a chat. And some evenings I will get a call when I am on my way home, checking that I am en route and when I will get home. She doesn't have friends in when we're not there (and is very good about that). And she hasn't yet moved on to getting the bus to the local town herself - she will before the summer, but an upset this summer on camp from another parent really knocked her confidence and set things back months.
If she had a half day from school, so home for maybe 6 hours, I would be happy to leave her but probably get home early. But not the whole day yet - she can't find enough things to entertain herself, and while she would cope, I think she would be lonely and upset before the end of the day.
But she